1. Field of the Invention
The present invention relates to electron beam lithography used when fabricating a semiconductor device, and more particularly, to an exposure method for correcting dimension variations in a pattern due to an electron beam rescattering effect occurring during electron beam exposure (hereinafter, xe2x80x9cfogging effectxe2x80x9d) and/or a loading effect, and a medium for recording the same.
2. Description of the Related Art
Electron beam lithography is used when forming an opaque layer on a mask substrate and patterning the opaque layer to have a desired pattern. In electron beam lithography, an electron beam resist is applied to the opaque layer, and a desired pattern is exposed to an electron beam and developed. Then, the opaque layer is etched using the electron beam resist pattern as a mask.
In general, the electron beam not only exposes a desired portion of the electron beam resist, but also is scattered, being reflected from the surface of the opaque layer, from the surface or the inside of the electron beam resist, or from a lower part of an object lens of an electron beam illuminator, or colliding with electrons of the electron beam resist, thereby exposing an undesired portion of the electron beam resist. Such scattered exposure results in a change in a critical dimension (CD) of a pattern. A change in the critical dimension of a pattern that is caused by exposure due to the electron beam being reflected from the surface or the inside of the electron beam resist or from the object lens of the electron beam illuminator is called a xe2x80x9cre-scattering effectxe2x80x9d or xe2x80x9cfogging effect.xe2x80x9d
Also, the critical dimension of a pattern changes when the opaque layer is dry-etched using the electron beam resist pattern as a mask after the development of the electron beam resist. This is called a xe2x80x9cloading effect.xe2x80x9d The density of area from which electron beam resist film is removed and lower opaque layer is exposed within a given area of the mask substrate is called xe2x80x9cloading density.xe2x80x9d The critical dimension of a portion having large loading density is larger than that of a portion having small loading density.
The fogging effect and the loading effect have been corrected by controlling exposure dose through additional exposure. FIG. 1 is a block diagram of an exposure method for correcting critical dimension variation of a pattern which has been commonly used. Referring to FIG. 1, a mask substrate is exposed according to a desired pattern (100). The mask substrate on which the pattern is formed is sectioned into mesh units and then L, a measure of the fogging effect and/or the loading effect, is calculated for each mesh unit with the following expression (1) (110). Additional exposure dose is determined referring to an L value calculated for the respective mesh units (120). Additional exposure dose must be comparatively increased for a mesh unit having a small L value and be comparatively decreased for a mesh unit having a large L value (130).                               L          ⁡                      (                          x              ,              y                        )                          =                              ∑                          i              ,              j                                ⁢                                    D              ⁡                              (                                  i                  ,                  j                                )                                      ⁢                          exp              [                              -                                                                                                    (                                                  x                          -                          i                                                )                                            2                                        +                                                                  (                                                  y                          -                          j                                                )                                            2                                                                            δ                    2                                                              ]                                                          (        1        )            
wherein x and y are coordinates of a mesh unit to be estimated and D (i,j) is exposure pattern density within the mesh unit whose coordinates are (i, j).
The effectiveness of the above method of correcting the critical dimension of a pattern has proven to be excellent. Nonetheless, the method has at least two drawbacks. Firstly, a throughput loss is incurred due to the additional exposure. Although the amount of a loss is different according to types of exposure tools, an additional exposure causes a delay in process time of roughly twenty minutes to one hour per mask.
Secondly, the critical dimension of a pattern is difficult to precisely correct because there are ten additional exposure stages needed for correction even in making a correction pattern and controlling exposure dose by defocusing an electron beam. In each stage, the amount of critical dimension correction is only approximately 3-4 nm.
To solve the above problems, it is an objective of the present invention to provide a correction exposure method for precisely correcting dimensional variations in a pattern due to the fogging effect and loading effect without a loss in throughput during electron beam exposure.
In accordance with the invention, there is provided an exposure method for correcting dimension variations in a pattern formed on a mask substrate during electron beam lithography. In the method, the mask substrate having a pattern is divided into mesh units and an L value for each mesh unit is calculated using the following formula:       L    ⁡          (              x        ,        y            )        =            ∑              i        ,        j              ⁢                  D        ⁡                  (                      i            ,            j                    )                    ⁢              exp        [                  -                                                                      (                                      x                    -                    i                                    )                                2                            +                                                (                                      y                    -                    j                                    )                                2                                                    δ              2                                      ]            
where x and y are coordinates of a mesh unit whose L value is to be calculated, and D(i,j) is an exposure pattern density within a mesh unit having the coordinates (i,j). Next, pattern dimension data regarding each mesh unit is corrected, so that dimensions for a mesh unit having a small L value become larger and dimensions for a region having a large L value become smaller. Then, the corrected pattern dimension data for each mesh unit is applied to an exposure tool.
Pattern dimension data is corrected by experimentally calculating the range of dimensional variations according to L for each mesh unit. Then, pattern dimensions in a mesh unit having a small L value are corrected by applying +bias to pattern dimension data of the mesh unit to increase the pattern dimension, and pattern dimensions in a mesh unit having a large L value are corrected by applying xe2x88x92bias to pattern dimension data of the mesh unit to decrease the pattern dimension,
wherein:
+bias=(Lxe2x88x92Lmin)*dimension variation range, and
xe2x88x92bias=(Lmaxxe2x88x92L)*dimension variation range,
wherein Lmax is a maximum value of L calculated and Lmin is a minimum value of L calculated.
The above correction method can be used in correcting dimension variations in a pattern formed on a mask substrate due to the loading effect or fogging effect. Further, it can be used in correcting dimension variations in a pattern due to the loading effect and the fogging effect. The values L and D can denote a loading effect and a loading density, respectively. Alternatively, the values L and D can denote a fogging effect and an exposure pattern density, respectively. Alternatively, the value L can denote a combined value of a fogging effect and a loading effect, and the value D can denote an exposure pattern density.
To achieve the objective, there is also provided a recording medium on which a computer program for performing the above exposure method is recorded and which is readable by a computer. The recording medium includes a program module for dividing the mask substrate having the pattern into mesh units and calculating L for each mesh unit using the following expression:       L    ⁡          (              x        ,        y            )        =            ∑              i        ,        j              ⁢                  D        ⁡                  (                      i            ,            j                    )                    ⁢              exp        [                  -                                                                      (                                      x                    -                    i                                    )                                2                            +                                                (                                      y                    -                    j                                    )                                2                                                    δ              2                                      ]            
wherein x and y are coordinates of a mesh unit of a mesh for which L is to be calculated and D(i,j) is an exposure pattern density within a mesh unit having the coordinates (i,j). The recording medium also includes a program module for correcting pattern dimension data regarding each mesh unit so that pattern dimensions for a mesh unit having a small L value are increased and pattern dimensions for a mesh unit having a large L value are decreased, and a program module for applying corrected pattern dimension data for each mesh.
Through the program module for correcting pattern dimension data, the range of dimensional variations in a pattern can be experimentally calculated according to L for each mesh unit and pattern dimensions in a mesh unit having a small L can be corrected by applying +bias to pattern dimension data of the mesh unit to increase the pattern dimension, and pattern dimensions in a mesh unit having a large L can be corrected by applying xe2x88x92bias to pattern dimension data of the mesh unit to decrease the pattern dimension,
wherein:
+bias=(Lxe2x88x92Lmin)*dimension variation range, and
xe2x88x92bias=(Lmaxxe2x88x92L)*dimension variation range,
wherein Lmax is a maximum value of L calculated and Lmin is a minimum value of L calculated.